Mariupol, Ukraine (CNN) -- It's a hot, sunny Sunday morning, and birds are chirping in the trees over the heads of children playing on swings and in a pile of sand in a small park in front of City Hall. Or what used to be City Hall, anyway.
Today, it's a burned-out husk of a building, the ground around it thick with ash and crunchy with broken glass, official documents strewn around and covered with footprints. Windows are shattered. Walls are stained black by smoke and fire.
A dozen or so young men lounge around on the front steps of the building, asserting that they are part of the militia of the Donetsk People's Republic. But they look more like drunks with nowhere else to go after a night out.
But they're not the only ones hanging around the remains of City Hall in Mariupol, recently the scene of clashes between supporters of the central government and backers of either independence or union with Russia for this part of eastern Ukraine.
Yevgeny Bulgakov, a steelworker, is here too, wearing his thick Ilyich factory work jacket despite the heat of the day. He's here to help re-establish order in the city, he said.
And indeed, despite the destruction of City Hall, the scene is much calmer than it was a month ago, when the building stood behind a makeshift barricades of tires, bricks and paving stones.
That's gone today. The only remnants are a coil of barbed wire discarded among spring flowers and a small pile of tires by the street corner.
Did the steelworkers bring calm?
Some are giving credit for the restoration of order here to the steelworkers. There are tens of thousands of them in this industrial city where factories spew brown and gray smoke along the road into town.
About 11,000 of them signed up to help patrol Mariupol along with local police, according to the company MetInvest, which employs them.
The patrols come alongside an agreement signed by a wide range of leaders in Mariupol to try to de-escalate the situation. The deal came five days after violence in the city left at least seven people dead and 40 wounded, according to Human Rights Watch.
The steelworkers are backed by their boss, Donetsk-based billionaire Rinat Akhmetov, who came out against both independence and union with Russia last week. Many of them are paid for the time they patrol, MetInvest said.
But steelworkers are not the only ones on patrol. They only make up about a third of the total volunteer force, locals say.
And hard-core supporters of independence for the region don't give them credit for restoring order. A group of about a dozen steelworkers was jeered as several hundred supporters of independence gathered for a march Sunday to mark the killings on May 9 that seem to have been a turning point in the city.
Hard questions for separatist leader
But the separatist crowd also has hard questions for the local separatist military commander, Andrey Borisov, an angular man with a shaggy beard and close-cropped hair under a beret.
They surrounded him and peppered him with questions as he smoked and sweated in the hot sun.
He didn't seem to be able to say who's in control.
"Who will govern? You will be the first one to come up to me when you don't have your pension paid. The transition of power is a complicated process," he said.
And he admitted that the separatists need more men.
"We need guys who are able to take arms and fight," he said to the crowd, composed mostly of people middle-aged and older, none of whom volunteered for the job.
That could be a problem for the self-declared local political leader, Denis Kuzmenko.
Kuzmenko vowed firmly Sunday that the people of Mariupol would not participate in Ukraine's presidential election scheduled to take place in a week.
The friendly, slightly chubby man wore a pistol in a holster on his hip as he spoke to journalists outside his headquarters, a tightly secured brick police station taken over by the separatists.
His words were firm.
"We consider trying to open up a polling station and trying to establish an opportunity to vote as a provocation. We will treat it as such," he said.
But can he carry out the threat? He all but admitted he doesn't have enough men to control the city when asked whether he needed the steelworkers to help maintain order.
"Of course we need everyone," he said, saying there are 50,000 steelworkers in the area, and that the majority support independence.
He denied there was a divide between "the steelworkers" and the people.
"They are patrolling because they support the Donetsk People's Republic and they want order," he said.
As Kuzmenko spoke, his security guard, a clean-cut man with shiny gray trousers, violet shirt and AK-47, came over to a journalist, tugged his arm and spoke English.
"Our citizens are the steelworkers," he said. "It is the same."
Erin McLaughlin and journalist Lena Kashkarova contributed to this report